If $f\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {\frac{{x\log \cos x}}{{\log \left( {1 + {x^2}} \right)}},x \ne 0}\\ {0,x = 0} \end{array}} \right.$, then

$f\left( x \right)$ is not continuous at $x = 0$

$f\left( x \right)$ is not continuous at $x = 0$ but not differentiable at $x = 0$

JEE MATHEMATICS MCQ: DIFFERENTIATION

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Analyzing +4 | -1

f\left( x \right) = \left\{ {\begin{array}{cccccccccccccccccccc} {\frac{{x\log \cos x}}{{\log \left( {1 + {x^2}} \right)}},x \ne 0}\\ {0,x = 0} \end{array}} \right.

, then

View answer and explanation

Correct option: B

f\left( x \right)

is not continuous and differentiable at

x = 0

Option D (None of these) is incorrect. The function is continuous and differentiable at x=0. The solution steps show the derivative exists and is -1/2.

JEE MATHEMATICS MCQ: DIFFERENTIATION

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